The Camp Nou outfit have fallen behind Atletico Madrid at the top of La Liga, and are now level on points with Real in second.
But Pique insists Barca have the quality to pull through and overcome the two capital clubs.
"Madriditis? That was fixed in the last decade," he told Spanish radio show Al Primer Toque. "(Real) Madrid have been a very successful club that has won many titles and nine European Cups. That gives them the best team of the last 100 years.
"But in the last 10 to 15 years we are there and are winning many titles in the present.
"We must remember the past, though. It's a rivalry that will last forever.
"A team is better if the other is better."
The reigning champions lost 3-2 at home to Valencia on Saturday, but Pique is believes that it was just a blip in an otherwise promising season, singling out Lionel Messi as the man to drive the club forward.
"I see Leo every day and I see a bestial desire to keep winning titles," he continued. "There was a game we lost at home, very tough, but we were still in a good moment.
"I talked to him and he made me realise that defeat still hurts and you realise you're hurt and you want more titles."
Pique's contract is due to expire in 2015, but the 27-year-old is confident of reaching an agreement to extend his stay.
"All will go well," he added. "With the change of president it;s unclear, but (Josep Maria) Bartomeu has already been in contact.
"I'm content. I know the club is my life."
